THERMAL ANALYSIS METHOD FOR CERAMIC MATRIX COMPOSITE (CMC) TURBINE VANE CONSIDERING MICRO-WOVEN STRUCTURE AND CHANGE OF DIRECTION OF FIBER BUNDLES

Abstract

A thermal analysis method for a ceramic matrix composite (CMC) turbine vane considering a micro-woven structure and a change of direction of fiber bundles: obtaining geometric characteristics of the fiber bundles of the internal woven structure of the CMC; establishing a micro-model of warp yarns and weft yarns of the woven structure and a CMC matrix; constructing a woven structural CMC turbine vane model with a micro-structure periodic width in a vane height direction; assigning an anisotropic thermal conductivity matrix varying with a vane profile; performing meshing; performing finite element calculation of a temperature field; and obtaining calculation results of the temperature field of the woven structural CMC turbine vane model, comparing the calculation results with calculation results based on a homogenization thermal analysis method for an equivalent thermal conductivity for analysis, and extracting and analyzing fluctuation characteristics of the temperature field of the woven structural CMC turbine vane.

Claims

1. A thermal analysis method for a ceramic matrix composite (CMC) turbine vane considering a micro-woven structure and a change of direction of fiber bundles, comprising the following steps: step I, obtaining geometric characteristics of the fiber bundles of the internal woven structure of the CMC based on an scanning electron microscope (SEM); step II, according to the geometric characteristics obtained in step I, combined with an actual thickness of the CMC turbine vane, establishing a micro-model of warp yarns and weft yarns of the woven structure and a CMC matrix; step III, according to geometric periodic characteristics of the woven structure, constructing a woven structural CMC turbine vane model with a micro-structure periodic width in a vane height direction; step IV, for the woven structural CMC turbine vane model constructed in step III, assigning an anisotropic thermal conductivity matrix varying with a vane profile; step V, meshing the woven structural CMC turbine vane model constructed in step III; step VI, performing finite element calculation of a temperature field on the woven structural CMC turbine vane model; and step VII, obtaining calculation results of the temperature field of the woven structural CMC turbine vane model, comparing the calculation results with calculation results based on a homogenization thermal analysis method for an equivalent thermal conductivity for analysis, and extracting and analyzing fluctuation characteristics of the temperature field of the woven structural CMC turbine vane.

2. The thermal analysis method for a CMC turbine vane considering a micro-woven structure and a change of direction of fiber bundles according to claim 1, wherein in step I, the geometric characteristics comprise section size characteristics and a fiber bundle spacing.

3. The thermal analysis method for a CMC turbine vane considering a micro-woven structure and a change of direction of fiber bundles according to claim 1, wherein in step III, in the woven structural CMC turbine vane model, a direction of the warp yarns changes along the vane profile, and the weft yarns are woven around the warp yarns.

4. The thermal analysis method for a CMC turbine vane considering a micro-woven structure and a change of direction of fiber bundles according to claim 3, wherein step III comprises: first sweeping a warp yarn section along a characteristic line of the vane profile to establish warp yarn characteristics at different thickness positions, and then interleaving a weft yarn section around the warp yarns in the vane height direction, wherein a spacing between the warp yarn and the weft yarn is a fiber bundle spacing.

5. The thermal analysis method for a CMC turbine vane considering a micro-woven structure and a change of direction of fiber bundles according to claim 1, wherein in step IV, the anisotropic thermal conductivity matrix of the warp yarns and the weft yarns varies with space of the vane profile through curvilinear coordinates in a Comsol-Multiphysics software mathematics module, local curvilinear coordinates varying with the vane profile are set for the warp yarns and the weft yarns inside the vane, and then based on the curvilinear coordinates, an anisotropic thermal conductivity in three directions of a local area are assigned to characterize spatial variation characteristics of the anisotropic thermal conductivity matrix.

6. The thermal analysis method for a CMC turbine vane considering a micro-woven structure and a change of direction of fiber bundles according to claim 1, wherein in step V, local mesh densification is performed in a dense area of the fiber bundles and an area at a junction of the fiber bundles and the CMC matrix.

7. The thermal analysis method for a CMC turbine vane considering a micro-woven structure and a change of direction of fiber bundles according to claim 1, wherein in step VI, convective heat transfer boundary conditions of the third kind are respectively applied to inner and outer surfaces of the woven structural CMC turbine vane model, and periodic boundary conditions are applied to upper and lower periodic structure surfaces, so as to perform the finite element calculation of the temperature field.

Description

BRIEF DESCRIPTION OF THE DRAWINGS

[0027] FIG. 1 is a turbine vane model of a CMC based on a micro-woven structure;

[0028] FIG. 2 is a distribution diagram of a local calculation coordinate system;

[0029] FIG. 3 shows distribution of a heat transfer coefficient on an outer surface of a vane;

[0030] FIG. 4 is a homogenized vane model based on an equivalent thermal conductivity;

[0031] FIG. 5 shows vane temperature distribution, where (a) is a homogenized vane; (b) is a woven structural vane; (c) is an outer surface of the homogenized vane; and (d) is an outer surface of the woven structural vane; and

[0032] FIG. 6 is a comparison diagram of temperature distribution on characteristic lines of two models of the woven structural vane and the homogenized vane.

DETAILED DESCRIPTION OF THE EMBODIMENTS

[0033] In view of the requirements of a thermal analysis method for a woven structural CMC turbine vane and considering the current thermal analysis for the CMC turbine vane, a homogenization method based on an anisotropic equivalent thermal conductivity is often used, which can better obtain regular characteristics of temperature field distribution of the CMC turbine vane. However, since the micro-woven structure is homogenized, the method cannot obtain fluctuation characteristics of a temperature field caused by the woven structure, and cannot meet the requirements of high-precision thermal analysis of the woven structural CMC turbine vane. Therefore, the present disclosure provides a thermal analysis method for a CMC turbine vane considering a micro-woven structure and a change of direction of fiber bundles, including the following steps.

[0034] Step I, geometric characteristics of the fiber bundles of the internal woven structure of the CMC are obtained based on an SEM. The geometric characteristics include section size characteristics and a fiber bundle spacing.

[0035] Step II, according to the geometric characteristics obtained in step I, combined with an actual thickness of the CMC turbine vane, a micro-model of warp yarns and weft yarns of the woven structure and a CMC matrix is established.

[0036] Step III, according to geometric periodic characteristics of the woven structure, a woven structural CMC turbine vane model with a micro-structure periodic width in a vane height direction is constructed. In the woven structural CMC turbine vane model, a direction of the warp yarns changes along the vane profile, and the weft yarns are woven around the warp yarns. First, a warp yarn section is swept along a characteristic line of the vane profile to establish warp yarn characteristics at different thickness positions, then a weft yarn section is interleaved around the warp yarns in the vane height direction, and a spacing between the warp yarn and the weft yarn is a fiber bundle spacing.

[0037] Step IV, for the woven structural CMC turbine vane model constructed in step III, an anisotropic thermal conductivity matrix varying with a vane profile is assigned. The anisotropic thermal conductivity matrix of the warp yarns and the weft yarns varies with space of the vane profile through curvilinear coordinates in a Comsol-Multiphysics software mathematics module, local curvilinear coordinates varying with the vane profile are set for the warp yarns and the weft yarns inside the vane, and then based on the curvilinear coordinates, an anisotropic thermal conductivity in three directions of a local area are assigned to characterize spatial variation characteristics of the anisotropic thermal conductivity matrix.

[0038] Step V, the woven structural CMC turbine vane model constructed in step III is meshed. Local mesh densification is performed in a dense area of the fiber bundles and an area at a junction of the fiber bundles and the CMC matrix.

[0039] Step VI, convective heat transfer boundary conditions of the third kind are respectively applied to inner and outer surfaces of the woven structural CMC turbine vane model, and periodic boundary conditions are applied to upper and lower periodic structure surfaces, so as to perform the finite element calculation of the temperature field.

[0040] Step VII, calculation results of the temperature field of the woven structural CMC turbine vane model are obtained, and compared with calculation results based on a homogenization thermal analysis method for an equivalent thermal conductivity for analysis, and fluctuation characteristics of the temperature field of the woven structural CMC turbine vane are extracted and analyzed.

[0041] The present disclosure is further described below with reference to embodiments and comparative examples.

Embodiment

[0042] The present embodiment takes a C3X vane as an example. The vane is made of a 2.5D woven structure composite. The size of a single cycle of a woven structure is length×width×height=10×4.8×3.3 mm. The material fiber bundle has a width of 1.6 mm, and a thickness of 0.2 mm A spacing between weft yarns in a length direction is 2 mm, a spacing between warp yarns in a thickness direction is 0.6 mm, and a weaving angle is 34°. A woven structural turbine vane as shown in FIG. 1 is established. The vane has an axial chord length of 78 mm, and a circumferential chord length of 145 mm. The woven structure has a cycle length of 10 mm in a vane height direction (Y). The vane is composed of an annular vane body and straight ribs. The straight ribs 1 and 2 divide the interior of the vane into three internal cooling channels, and the ribs and the vane both have a thickness of 3.3 mm.

[0043] In view of the above woven structural CMC turbine vane model, a free tetrahedral mesh in Comsol-Multiphysics is used for meshing. A largest mesh element selected is 0.8 mm, a smallest element is 0.1 mm, a maximum growth rate is 1.45, and a curvature factor is 0.5. The mesh is refined in an area where a curvature of the woven structure changes greatly to avoid local twisting and inverted curved surface elements in the mesh. The final mesh amount of the woven structural vane is 10106385.

[0044] The woven structural vane contains 2696 different physical domains. In addition to the isotropic matrix, the woven yarn has obvious anisotropic characteristics, and the warp yarns and the weft yarns have different spatial distribution in the vane, resulting in a spatial deviation between the anisotropic thermal conductivity direction coordinate system of the warp yarns and the weft yarns and the calculation coordinate system, and main directions of the thermal conductivity of the warp yarns and the weft yarns need to be spatially converted to set the thermal conductivity. In the present embodiment, a local coordinate system varying with spatial distribution is set for the warp yarns and the weft yarns inside the vane body through curvilinear coordinates in a Comsol-Multiphysics mathematics module, as shown in FIG. 2. For the warp yarns and the weft yarns, only the thermal conductivity in three directions in the local coordinate system of their own needs to be given.

[0045] Then boundary conditions of the third kind are applied to a surface of the vane for calculation, and reference may be made to experimental results of the working condition 4521 in the literature (L. D. Hylton, M. S. Mihelc, E. R. Turner, et al. Analytical and Experimental Evaluation of the Heat Transfer Distribution Over the Surfaces of Turbine Vane[R]. America: National Aeronautics and Space Administration NASA Lewis Research Center, 1983:1-225). The experimental data of an outer surface of the vane under this working condition is selected as a heat transfer coefficient of the outer contour of the woven structural CMC turbine vane, as shown in FIG. 3. FIG. 3 shows distribution of the heat transfer coefficient on a suction surface and a pressure surface respectively, where the abscissa is a ratio of a distance from a point on the suction surface (or pressure surface) to a leading edge and an entire arc length of the suction surface (or pressure surface), and the ordinate is the heat transfer coefficient. According to the previous section, when the spatial distribution of the thermal conductivity of the homogenized vane in the calculation coordinate system is solved, expressions of the suction surface and the pressure surface are fit, and a point corresponding to the experimental data on an outer contour line is obtained by solving the curvilinear integral and the value of the point is assigned. For the area where no experimental data is given, heat transfer coefficients at front and back ends of the area are used for linear interpolation, and finally the distribution of the heat transfer coefficient on the entire outer contour of the vane is obtained. The above work is completed in Matlab to obtain an equation file of the heat transfer coefficient of the outer contour, which can called by the Comsol link with Matlb module and used as an external heat transfer boundary condition. The temperature of the outer contour is a mainstream inlet temperature, and is 818 K.

[0046] The vane is constructed based on the shape of the C3X vane. The internal cooling channel of the vane is divided into three cooling channels by the ribs, which are respectively marked as a cooling channel 1, a cooling channel 2, and a cooling channel 3. Specific values of the wall heat transfer coefficient and the corresponding gas temperature are summarized in Table 1:

TABLE-US-00001 TABLE 1 Heat transfer boundary conditions of internal cooling channel of woven structural vane Cooling channel 1 Cooling channel 2 Cooling channel 3 Heat Heat Heat transfer transfer transfer Temper coefficient Temper coefficient Temper coefficient ature- (W/ ature- (W/ ature- (W/ (K) (m.sup.2 .Math. k)) (K) (m.sup.2 .Math. k)) (K) (m.sup.2 .Math. k)) 335 439.5 330 550 350 860.8

COMPARATIVE EXAMPLE

[0047] In order to compare the difference between the thermal analysis model established by the present disclosure and the homogenization thermal analysis model based on the equivalent thermal conductivity for analysis, a homogenized vane model as shown in FIG. 4 is also established here using a numerical method in the literature (Z. Tu, J. K. Mao, H. Jiang, et al. Numerical method for the thermal analysis of a ceramic matrix composite turbine vane considering the spatial distribution of the anisotropic thermal conductivity, Applied Thermal Engineering, 2017, 127:436-452) to obtain a homogenized temperature field of a woven structural CMC turbine vane.

[0048] FIG. 5 shows a schematic diagram of temperature distribution of the homogenized vane and the woven structural vane. It can be seen from FIG. 5 that the woven structural vane has an overall temperature significantly higher than that of the homogenized vane, and the temperature field distribution on the surface of the homogenized vane is relatively uniform. From the temperature distribution on the outer surface of the vane, it can be further seen that the surface temperature of the woven structural vane has obvious temperature fluctuation characteristics, the temperature is alternately distributed with the woven structure, and the two vanes have the maximum and minimum temperature at the same position on the outer surfaces. However, the temperature is very different. The maximum surface temperature of the woven structural vane is 42.683 K higher than that of the homogenized vane. The difference between the minimum temperature of the two is 72.631 K, which is significant.

[0049] FIG. 6 shows temperature distribution of the homogenized vane and the woven structural vane on characteristic lines of the leading edge, suction surface, pressure surface, and trailing edge of the vane in the vane height direction. Both ends of the characteristic line pass through a matrix area and the middle passes through a woven area. From FIG. 6, it can be more clearly found that the temperature of the woven structural vane is overall higher than that of the homogenized vane. The temperature of the homogenized vane in the vane height direction is basically unchanged, while the temperature on the characteristic line of the woven structural vane is high at both ends and low in the middle. The temperature fluctuation is obvious. Further analysis of the data on the characteristic line shows that the minimum difference between the average temperature on the characteristic line of the homogenized vane and the average temperature on the characteristic line of the woven structural vane is 38.7 K, and the maximum difference between the average temperature is as high as 93.3 K. The maximum temperature change of the woven structural vane on the characteristic line is close to 35 K, and the maximum amplitude of temperature fluctuation on the characteristic line also exceeds 18 K, which has significant inhomogeneity and severe temperature fluctuation.

[0050] Therefore, compared with the comparative example, the embodiment can more accurately obtain the temperature field fluctuation information of the turbine vane caused by the material woven structure, and further improve the simulation accuracy of the woven structural CMC turbine vane.

[0051] The foregoing descriptions are only preferred implementations of the present disclosure. It should be noted that several improvements and modifications may further be made by a person of ordinary skill in the art without departing from the principle of the present disclosure, and such improvements and modifications should also be deemed as falling within the protection scope of the present disclosure.